# An inspired problem (but I shouldn't say what inspired me)

Calculus Level 4

$\large \mathscr{E} = \displaystyle {\huge \int \limits_{0}^{\sqrt{3}}} \frac{2(1+x^2) - (2x)^2}{(1+x^2)^2 \sqrt{1- \left(\dfrac{2x}{1+x^2} \right)^2}} \, dx$

If $$\mathscr{E}$$ can be represented in the form $$\dfrac{a\pi}{b}$$, with $$a$$ and $$b$$ being coprime positive integers, find $$a + b$$.

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